Setting Up A Minimal Sculpting Environment With An Image Area
Ok, here we go: 
1. Remove UV Screen 
This may sound contradictory, but necessary to remove the timeline. Blender is weird like this and will only collapse a section if their is only one section spanning the width of it above it. Remember to collapse a section pull on those little three lines in the top corner
 
2. Collapse Timeline 
Pull on the three corners in the 3d view as shown in the image.
 
3.Right Panel 
Remember step one when we collapsed the UV screen to collapse the timeline? Well we have to do this again to collapse the right panel. First pull down then up as depicted in the image below to remove the outliner. 

4.Finishing up 
Now, press T to close the tool panel. Next pull the top three corners of the 3d view toward the right panel to collapse it. To remove that top bar pull on the three lines below the info icon and pull down, then up. Finally, Pull the 3d view corner again to the left to open up another 3d view. You can change it to UV image editor by clicking the icon. 
 
 
 
Further Reading 
How to close view windows? 
Arranging Areas - Blender Reference Manual 
Simple, Nice Explanation On BSE 
Great Youtube Video